anonymous
  • anonymous
I am having the most difficult time trying to understand a problem with the formula a=pe^rt, where A=amount accumulated, p=principal, r=interest rate, and t=time in yrs. What principal should be deposited at 7.405% to ensure the account will be worth $18,000 in 11 years
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
18,000 = p(1+.07405)^11
anonymous
  • anonymous
So 18,000=(1p+7405p)^11, right?
anonymous
  • anonymous
First step would be to add (1 + .07405) to get 1.07405 Then take that to the ^11

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anonymous
  • anonymous
2.194166065
anonymous
  • anonymous
I thought the formula was A= p/e^rt
anonymous
  • anonymous
Good now you have 18,000 = 2.194166065p so divide both sides by 2.194166065
anonymous
  • anonymous
8203.572322= p
anonymous
  • anonymous
or $8203.57?
anonymous
  • anonymous
OK.. we can do it your way... just a minute.
anonymous
  • anonymous
18,000 = P e^(.07405*11) 18,000 = Pe^.81455 18,000 = P 2.258 Divide by 2.258 $7971.66
anonymous
  • anonymous
How do you calculate e?
anonymous
  • anonymous
I plugged it into the calculator... I have an e^x key.
anonymous
  • anonymous
Wait just a minute
anonymous
  • anonymous
Also the ln key right?
anonymous
  • anonymous
Ok, I got the same thing you got this time.
anonymous
  • anonymous
I am not used to the e function.. here is an example, I will do yours for you following this example So 130000 = 1949 e^(.00835 t) Take logs of both sides: ln 130000 = ln 1949 e^(.00835 t) = ln 1949 + ln e^(.00835 t) = ln 1949 + .00835 t t = (ln 130000 - ln 1949) / .00835 = (ln 130000/1949) / .00835 which you have to calculate using a calculator
anonymous
  • anonymous
18,000 = Pe^(.07405 * 11) 18,000 = Pe^.81455 ln 18000 = ln P + ln(e^.81455) ln 18000 = ln P + .81455 9.79813 - .81455 = ln P 8.98358 = ln P e^8.98358 = e^ (ln P) $7971.12 = P
anonymous
  • anonymous
ok. It was the "e" part that was throwing me off. But what you and I got is what the book has also.
anonymous
  • anonymous
Great... A little out of my league... but I am glad we got it.
anonymous
  • anonymous
Now, with the formula with A =p(1+r/n)^nt A = $982500 p+71500, t=17yr
anonymous
  • anonymous
Don't we have to know either r or n?
anonymous
  • anonymous
I have 98, 2500=71, 500(1+r/n)^17. Do you know how I would find r/n?
anonymous
  • anonymous
R is what they are asking for. R is a percent
anonymous
  • anonymous
What is n?
anonymous
  • anonymous
Here's the question: For compound interest accts, the amount A accumulated or due depends on the principal p, interest rate r, number of compounding per year n, and the time t in years according to the formula A=p(1 + r/n)^nt. Find the r given A=$98, 250, p=71,500, and t=17 yr with interest compound monthly
anonymous
  • anonymous
compounded monthly means that n = 12
anonymous
  • anonymous
982,500 = 71500(1 + r/12)^12*17
anonymous
  • anonymous
oh, because 12 represent the "per year"
anonymous
  • anonymous
982,500 = 71,500(1 + r/12)^204
anonymous
  • anonymous
divide both sides by 71,500
anonymous
  • anonymous
13.7412587 = (1 + r/12)^204
anonymous
  • anonymous
13. 74128874=(1+r/12)^204
anonymous
  • anonymous
Now you have to get rid of the ^204 you do that by taking the 204th root of both sides. Use the x sqrt(y) key on your calculator
anonymous
  • anonymous
1.012927965 = 1 + r/12
anonymous
  • anonymous
Subtract 1 from both sides
anonymous
  • anonymous
.012927965 = r/12
anonymous
  • anonymous
multiply both sides by 12
anonymous
  • anonymous
12.155 = r
anonymous
  • anonymous
ON the step with the sq rt of 13.7412587 I got an error msg
anonymous
  • anonymous
Your saying 204 sq rt 13.7412587 correct?
anonymous
  • anonymous
You are not taking the sqrt root.. Find the key that has x sqrt(y) type in 13.7412587 hit the xsqrt(y) key and then type in 204 and hit enter
anonymous
  • anonymous
I dont believe I have that key
anonymous
  • anonymous
Are you operating a TI-84?
anonymous
  • anonymous
NO.. just a calculator on my computer the basic one..
anonymous
  • anonymous
Let me see if I can find a TI-84 on line and tell you what it looks like
anonymous
  • anonymous
How about under MATH option 5 does it show an x and then a radical sign
anonymous
  • anonymous
yes
anonymous
  • anonymous
You want the x to be the 204 and under the radical sign to be the 13.xxxxxx Try it and see if you can get what I got.
anonymous
  • anonymous
YES!!!! I got it! such a relief! thank you very much

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